Communication systems, spectral analysis, RADAR and SONAR transmit a signal which reaches, either reflected or not, the receiver after having traversed a transmission medium. This medium behaves like a linear filter with a response to the frequency H(ω) or temporal h[n] impulse. To enable the process of recovering the emitted information, most communication systems make it indispensable to eliminate the effects caused by the transmission medium on the emitted signal s[n]. This process is known as equalization. The response in frequency can also be used to carry out spectral analysis of the medium and to thus obtain information on the physical properties thereof.
The channel acts as a filter and distorts the signal. Noise n[n] due to perturbations in the channel, thermal noise or other signals interfering with the emitted signals, must be considered. In conclusion, the received signal r[n] can be modeled as:r[n]=s[n]*h[n]+n[n]  (1)where * represents the convolution operation. A filter with impulse response f[n] is required to eliminate the distortion introduced by the medium in the signal, such that:r[n]*f[n]≈s[n]  (2)
In other words, the received signal must be as similar as possible to the emitted signal. This requirement can never be fully met due to the fact that neither noise n[n] nor distortion is completely eliminated.
In order for equalization to be the best possible equalization, it is necessary to know the medium a priori. In other words, it is necessary to analyze h[n] of the medium to be able to counteract the distortion effects. There are two methods for achieving this objective:                Static equalizers: their properties do not change over time.        Adaptive equalizers: they are adapted to temporal variations of the distortion of the medium.        
The main problem with the first equalizers is that they are more generic and do not solve the particular problems of each situation. Adaptive equalizers respond better to variations of the medium, but their implementation is more complicated and they are very sensitive to noise.
For both equalizers it is still indispensable to know the transmission medium. The better the modulation of the transmission medium, the greater the precision that will be obtained when restoring the emitted signal. The ideal method for analyzing the medium consists of transmitting a delta and analyzing the received signal, i.e. obtaining the impulse response. This is achieved at the digital level by emitting a Krönecker delta δ[n]:s[n]=δ[n]r[n]=h[n]+n[n]  (3)
As can be observed, the received signal has information on the impulse response h[n] contaminated with additive noise.
The need for a technique allowing on one hand efficiently emitting a Krönecker delta, and on the other reducing the noise of the received signal, can be deduced from the foregoing. Sending a Krönecker delta directly is very complex because it requires high peak power. As will be seen, a very precise model of the transmission medium and the distortion it causes can be obtained by maintaining these two premises.
The characteristics extracted from the model of the medium can be used to equalize same in communications applications, or to analyze the physical characteristics thereof, as is the case of discriminating between different types of objectives in SONAR and RADAR systems, or carrying out spectral analyses for extracting physical-chemical properties, as is used in spectroscopy.
No patent or utility model the features of which are the object of the present invention is known.